A New Analysis of the Time-Fractional and Space-Time Fractional-Order Nagumo Equation
Bibliographic record
Abstract
In this paper, we present an algorithm by using the Adomian Decomposition Method (ADM) in order to solve the time-fractional Nagumo equation and the space-time fractional-order Nagumo equation. In the space-time fractional case, we expand the \(tanh(\cdot)\) initial condition in the basis functions \(e^{−n\zeta}\). The fractional-order derivative could then be easily calculated. An important point in our investigation is that many earlier authors avoided this initial condition as there was no direct method to calculate its fractional derivative. We have studied the convergence analysis and applied it to the time-fractional Nagumo equation and the space-time fractional-order Nagumo equation. We compare the ADM solution with the exact solution and find a very good agreement. We also graphically illustrate the behavior of the ADM solutions.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".